Table Of ContentSPRINGER BRIEFS IN PHILOSOPHY
Jan Willem Wieland
Infinite Regress
Arguments
SpringerBriefs in Philosophy
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Jan Willem Wieland
Infinite Regress Arguments
123
Jan WillemWieland
VUUniversityAmsterdam
Amsterdam
The Netherlands
ISSN 2211-4548 ISSN 2211-4556 (electronic)
ISBN 978-3-319-06205-1 ISBN 978-3-319-06206-8 (eBook)
DOI 10.1007/978-3-319-06206-8
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Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Two Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Overview of Classic Cases. . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Two Desiderata. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 The Paradox Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Classic Instances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Logical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 The Failure Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1 Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Classic Instances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.5 Logical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4 Case Study: Carroll’s Tortoise. . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1 The Renewed Tortoise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 Stage Setting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3 Four Solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.4 Three Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.5 Concluding Remark. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5 Case Study: Access and the Shirker Problem . . . . . . . . . . . . . . . . 53
5.1 Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2 The Loophole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.3 Paradox Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
v
vi Contents
5.4 Failure Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Chapter 1
Introduction
1.1 Overview
Infinite regress arguments (henceforth IRAs) are powerful arguments and fre-
quently used in all domains of philosophy. They play an important role in many
debates inepistemology,ethics,philosophyofmind,philosophy oflanguage, and
metaphysics.Inhistoricaldebates,theyhavebeenemployed,forexample,against
thethesisthateverythinghasacauseandagainstthethesisthateverythingofvalue
is desired for the sake of something else. In present-day debates, they are used to
invalidate certain theories of justification, certain theories of meaning, the thesis
that knowledge-how requires knowledge-that, and many other things.
Indeed, there are infinite regresses of reasons, obligations, rules, relations and
disputes, and all are supposed to have their own moral. Yet most of them are
involved in controversy. Hence the question is: what exactly is an IRA, and how
should such arguments be evaluated? This book answers these questions and is
composed as follows:
• Chapter 1 introduces the topic, presents an overview of classic IRAs, and
explains what we should expect from theories about IRAs.
• Chapters 2 and 3 summarize two theories of IRAs that have been presented in
the literature: namely The Paradox Theory and The Failure Theory.
• Chapters 4 and 5 concern two case studies which illustrate the general insights
about IRAs presented in the previous chapters in some detail.
Thisbookisofmetaphilosophicalnature.Itisabouthowphilosopherscanand
should proceed in their inquiries. Indeed: what steps can and should philosophers
taketodefendtheirviews?IRAs,then,arearguablyoneofthemainphilosophical
argumentation techniques (that is, next to thought experiments).
The book’s ultimate aim is to make a difference to the philosopher’s practice.
Particularly, the hope is that from now on disputes about any particular IRA
(concerning what it establishes, or concerning whether it can be resisted) will be
moreclearlymotivated,andindeedmoreclearlyframed,intermsoftheguidelines
outlined in what follows.
J.W.Wieland,InfiniteRegressArguments,SpringerBriefsinPhilosophy, 1
DOI:10.1007/978-3-319-06206-8_1,(cid:2)TheAuthor(s)2014
2 1 Introduction
I am grateful to many colleagues for advice. Special thanks go to: Arianna
Betti, Bert Leuridan, Anna-Sofia Maurin, Francesco Orilia, Benjamin Schnieder,
Maarten Van Dyck, Erik Weber, and René van Woudenberg. Thanks also to Jon
Sozek for the language edit, to the Flemish and Dutch science foundations for
financialsupport,andtotherefereesandeditorsofmyarticlesonwhichthisbook
is based (see Wieland 2013a, b, c, 2014).
1.2 Two Examples
To introduce the topic, let us consider two classic examples: Juvenal’s guardians,
and the ancient (yet timelessly relevant) Problem ofthe Criterion.1 Famously, the
Roman poet Juvenal posed the question: ‘‘But who will guard the guardians?’’
(Satire6.O29-34).TheIRAsuggestedbythisquestioncouldbespelledoutintwo
different ways:
Supposeyouwanttohaveyourpartnerguardedsothatheorshecannolongercommit
unfaithfulacts.Asasolution,youhireaguardian.Yet,asithappenswithguardians,they
cannot be trusted either. So a similar problem occurs: you want to have the guardian
guarded.Asasolution,youhireanotherguardian.Regress.Hence,hiringguardiansisa
badsolutiontohaveyourpartnerguarded.
Suppose that your partner is unreliable, that all unreliable persons are guarded by a
guardian, and that all guardians are unreliable. This yields a regress which is absurd.
Hence,eitheritisnotthecasethatallunreliablepersonsareguardedbyaguardian,oritis
notthecasethatallguardiansareunreliable.
Inthesecondcase,butnotinthefirst,thenotionof‘absurdity’hasanimportant
role.Thefactthatacertainregressisabsurddoesnotfollowfromassumptionsthat
generate the regress, and has to be argued for independently. Moreover, if the
regress is not absurd, then none of those assumptions have to be rejected. The
differences between these reconstructions will become clear later on, yet, as we
willsee,inprinciplebotharelegitimatereconstructions.HereistheProblemofthe
Criterion drawn from the ancient sceptics, a well-known case that inspired many
further similar problems:
In order to decide the dispute that has arisen […], we have need of an agreed-upon
criterion by means of which we shall decide it; and in order to have an agreed-upon
criterionitisnecessaryfirsttohavedecidedthedisputeaboutthecriterion.[…]Ifwewish
todecideaboutthecriterionbymeansofacriterionweforcethemintoinfiniteregress.
(Sextus,OutlinesofPyrrhonism,2.18–20)
Suppose, for example, that you want to settle a dispute about whether Juvenal
had a wife. To do so, you introduce another proposition, such as that Juvenal has
been banished his whole life and so could not have had a wife. Of course, this
1 Forthefirstexample,cf.Hurwicz(2008).Forthesecond,cf.Chisholm(1982,Chap.5),Amico
(1993),Lammenranta(2008).
1.2 TwoExamples 3
second proposition is disputable too. To settle that new dispute, you introduce a
third proposition, say that the sources about Juvenal’s banishment are highly
reliable. Of course, this third proposition is disputable too, and so on into the
regress.
Generally, the setting is you have to decide whether a certain proposition p is
true. You can do this critically, i.e. by a proof, or uncritically. If you do it
uncritically,thenyourdecisionisarbitraryandwillbediscredited.Butifyoudoit
criticallyanduseacriterionc todecidewhetherpistrue,youneedfirsttodecide
1
whether c correctly rules what is true and what is not. Again, there are two
1
options: you can do this critically, or not. If the latter, your decision will be
discredited. So you do it critically, and refer to a meta-criterion c which deter-
2
mineswhatcriteriacorrectlydeterminewhatistrueandwhatisnot.Butnowyou
needfirsttodecidewhetherc correctlydeterminesthecorrectcriteria.Again,you
2
can do this critically, or not. And so on.2
Again, the pattern can be described in two, slightly different ways:
Supposeyouwanttosettlethedisputeaboutsomeissue.Asasolution,youintroducea
criteriononthebasisofwhichitcanbesettled.Yet,thatcriterionisdisputabletoo.Soa
similarproblemoccurs:youwanttosettlethedisputeaboutthatcriterion.Asasolution,
youintroduceanothercriterion.Regress.
Suppose that at least one dispute is settled, that disputes are settled only if there is an
agreed-uponcriteriononthebasisofwhichtheyaresettled,andthatthereareagreed-upon
criteriaonlyifthedisputesaboutthemaresettled.Regress.
Now the question is what conclusion should be drawn from such a regress of
criteria.Doesitfollowthatonecannotsettlealldisputes?Orthatonecannotsettle
even one dispute? The second conclusion is clearly stronger than the first: if one
fails to settle all disputes, one might still settle many of them; yet if one fails to
settle any dispute, one automatically fails to settle all of them. As we will see in
thisbook,thereareinfactfourpossibleconclusionsIRAscanhave(andallrequire
their own kind of support):
• torefuteanexistentiallyquantifiedstatement,forexamplethestatementthat
at least one dispute is settled;
• torefuteauniversallyquantifiedstatement,forexamplethestatementthatfor
alldisputesitholdsthattheyaresettledonlyifthereisanagreed-uponcriterion
to settle them;
• todemonstratethatacertainsolutionfailstosolveauniversallyquantified
problem, for example that the given solution fails to settle all disputes;
2 Actually,theProblemoftheCriterionmightalsoinvolveacircularity,ratherthanaregress.In
thatcase,youprovethatc correctlydetermineswhatistrueandwhatisnotbyshowingthatit
1
predictstherightresults.Here,youalreadyknowwhatistrueandwhatisnot,andsowhetherpis
true or not. This is circular, for we started from the situation where you still have to decide
whetherpropositionpistrue.
4 1 Introduction
• to demonstrate that a certain solution fails to solve an existentially quan-
tified problem, for example that the given solution fails to settle even one
dispute.
Thus IRAs can be used for these four different purposes. Before explaining in
Chaps. 2and3howIRAsofthese fourkindswork,Iwillprovideanoverviewof
twelvemainclassicIRAs.Inthisoverview,Iwillsidesteptheissueinwhichofthe
four ways the given case should best be understood, and simply opt for one
specific reconstruction(but,aswillbecomeclear later,alternative reconstructions
of the cases are possible).
1.3 Overview of Classic Cases
Plato’sThirdMan
SupposeanythingislargeonlyifitpartakesoftheformLargeness,thatLargenessisitself
large,andthatformsaredistinctfromanythingthatpartakesofthem.Thisyieldsaregress
thatisabsurd.Hence:itisnotthecasethatanythingislargeonlyifitpartakesoftheform
Largeness.
Source:Parmenides,132a–b
Aristotle’sHighestGood
Supposeanythingisgoodonlyifwedesireitforthesakeofsomethingelsethatisgood.
Thisyieldsaregressthatisabsurd.Hence:atleastonethingisgoodandnotdesiredfor
thesakeofsomethingelsethatisgood,i.e.thehighestgoodthatisdesiredforthesakeof
itself.
Source:NicomachenEthics,1094a
Sextus’ Reasons
Supposethatsomepropositionsarejustifiedtosomeoneandthatpropositionsarejustified
tosomeoneonlyifthatpersonhasreasonsforthemwhicharethemselvesjustifiedtothat
person.Thisyieldsaregressthatisabsurd.Hence:eitheritisnotthecasethatalljustified
propositionsaresupportedbyreasonswhicharethemselvesjustifiedpropositions,orno
propositionisjustifiedtoanyone.
Source:OutlinesofPyrrhonism,1.166–7
Aquinas’CosmologicalArgument
Supposethateveryfiniteandcontingentbeinghasacause,andthateverycauseisafinite
and contingent being. This yields a regress that is absurd. Hence: it is not the case that
everycauseisafiniteandcontingentbeing.Theremustbeafirstcausewhichisnotfinite
orcontingent,namelyGod.
Source:SummaTheologica,bookI,v.2,Sect.3
